Step-by-step explanation:
[tex]y = \sqrt{x + 7} - 1[/tex]
Replace x and y.
[tex]x = \sqrt{y + 7} - 1[/tex]
Solve for y.
[tex]x + 1 = \sqrt{y + 7} [/tex]
Square both sides.
[tex](x + 1) {}^{2} = y + 7[/tex]
[tex](x + 1) {}^{2} - 7 = y[/tex]
This is the inverse function or you can also say
[tex] {x}^{2} + 2x - 6 = y[/tex]
